[tex]x = (\frac{1}{2})^{0.2} = (2^{-1})^{0.2} = 2^{-0.2}\\y = 16^{0.2} = (2^{4})^{0.2} = 2^{0.8}\\z = \sqrt[4]{8} = (2^{3})^{\frac{1}{4}} = 2^{ \frac{3}{4}}=2^{0.75}\\\\xy = 2^{-0.2}*2^{0.8}=2^{0.8-0.2} = 2^{0.6}\\xz = 2^{-0.2}*2^{0.75} = 2^{0.75-0.2} = 2^{0.55}\\yz = 2^{0.8}*2^{0.75}=2^{0.8+0.75} = 2^{1.55}\\\\0.55 < 0.6 < 1.55\\2^{0.55} < 2^{0.6} < 2^{1.55}\\xz < xy < yz[/tex]
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[tex]x = (\frac{1}{2})^{0.2} = (2^{-1})^{0.2} = 2^{-0.2}\\y = 16^{0.2} = (2^{4})^{0.2} = 2^{0.8}\\z = \sqrt[4]{8} = (2^{3})^{\frac{1}{4}} = 2^{ \frac{3}{4}}=2^{0.75}\\\\xy = 2^{-0.2}*2^{0.8}=2^{0.8-0.2} = 2^{0.6}\\xz = 2^{-0.2}*2^{0.75} = 2^{0.75-0.2} = 2^{0.55}\\yz = 2^{0.8}*2^{0.75}=2^{0.8+0.75} = 2^{1.55}\\\\0.55 < 0.6 < 1.55\\2^{0.55} < 2^{0.6} < 2^{1.55}\\xz < xy < yz[/tex]